The function f(x)=x²+2x-15/x²-4x+9, x R is [6 Apr 2024 Shift 1]

Correct Answer is : neither one-one nor onto.

Correct Answer is : neither one-one nor onto.

Test Index

Functions Part 2

Section: Mathematics

Question : 42 of 73

Marks: +1, -0

The function

f(x)=\frac{x^2+2x-15}{x^2-4x+9}, x\in R

Solution: 👈: Video Solution

NTA Ans. (3)

Ans. Bonus

f(x)=\frac{(x+5)(x-3)}{x^2-4x+9}

Let

g(x)=x^2-4x+9

D<0

g(x)>0\;\text{ for }\;x\in R

\therefore \left[\begin{array}{l} f(-5)=0 \\ f(3)=0 \end{array}\right].

So,

f(x)

is many-one. again,

yx^2-4xy+9y=x^2+2x-15

x^2(y-1)-2x(2y+1)+(9y+15)=0

\;\;\text{ for }\;\forall x\in R\Rightarrow D\ge 0

D=4(2y+1)^2-4(y-1)(9y+15)\ge 0

5y^2+2y+16\le 0

(5y-8)(y+2)\le 0

y\in[-2,\frac{8}{5}]\;\text{ range }\;

Note : If function is defined from

f: R\longrightarrow R

then only correct answer is option (3)

\Rightarrow

Bonus

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